Ian pretty much nailed it in his first post.
However, here's my elaborated take on the issue:
The quality that determines the the longevity of an optical disc:
1. optical disc quality (bonding quality, refletive layer material, dye layer material, label side materials, general QA of batch variability)
2. burner quality (low level) and compatibility with the burned media (firmware, burning strategy, optics, etc)
3. burning speed (i.e. not always the lowest speed, but right speed with the right strategy for the right media)
The above three pretty much decide the starting point for media longevity (i.e. low level burned disc characteristics, error counts and physical/chemical stability).
If any of the first three is seriously compromised you may end up with a disc that is not even worth archiving in the first place.
Then on to the archival
4. Archival, which includes, but is not limited to: protection from:
- noxious gases (sulphur compounds, ozone and general air pollutants)
- acidity (from various plasticicers used in jewel cases and cd sleeved folders that are not of archival quality)
- solvents (from various plastic manufacturing processes, sometimes wrongly chosen cd markers and even human skin contact, because grease can be a solvent too)
- radiation: namely infrared (heat) and UV radiation, but just plain "visible spectrum light" as well
- temperature (both absolute high/low temps and temperature changes): ideal is between 20-25 and no big changes
- humidity: relative humidity should be controlled and should not change quickly
- physical stress (bending, vertical uniform pressure, straching, etc)
- archival materials/storage containers used (which may contain hazards in addition to the above)
The above pretty much determines how long a disc can survive, until it starts to oxidizate, delaminate, loose it's dye stability or otherwise fail.
5. Handling determines how well the disc can survive, once it is taken from archival to intermediate use again. This includes handling the discs (fingerprints, bending, writing, scratching, read spinning speeds, labelling, etc).
6. Selection of readers determines the disc longevity in practical terms as well. If you have a pristine disc that has great low level values and intact data, but absolutely no-good readers then the data on the disc is pretty much irrelevant.
So, a good archival also takes into account the fact that a sufficient reader (physical level device) along with logical level file format support is still available at the time when the media needs to be taken from archives and read back again.
That's about it in short.
The longer list would include recommendations and guidelines, which can be gathered from NIST, OSTA and archival specialist publications.
Now as to the question how many years will dvd discs last?
It all depends on the above, but using the best discs, burners, storage and processes, they could ideally last for decades.
However at this point, nothing is sure, except the fact that dvds I burned more than 3 years ago are still functioning without any problems (high quality burners/high quality media/proper storage).
PS Many people are not aware of this, but a lot of the el-cheapo jewel cases are in fact worse for archival of cd/dvd discs than just putting them in a decent archival sleeved folder or even paper bags. Why? Because the plasticicers used with many ABS compound jewel cases cause the acidity inside the case to rise and start the slow but steady delamination/oxidisation of the disc.